On Impedance Based RF Dielectric Sensors and Applications in Agricultural Materials

A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL

OF THE UNIVERSITY OF MINNESOTA BY

Joshua D. Braun

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

Dr. Jonathan Chaplin

August 2010

© Joshua D. Braun 2010

i

Acknowledgements I would like to thank my advisor, Dr. Jonathan Chaplin whose guidance and support inspired me to ask the questions. I would also like to thank the many people who assisted me in my studies and research, especially my committee members. And to the many others who shared their knowledge graciously, thank you.

ii

Dedication For Beth, whose steadfast encouragement always brings out my best, and for Laura, whose curiosity inspires me.

iii

Abstract Increasing numbers of commercially available sensors claim to use the dielectric

response of grains and other agricultural materials to sense moisture and additional

properties. A review of past and current research in this area gives a basis for

investigating the efficacy and potential of one such instrument. A variety of materials,

including corn, soybeans, wheat, ground feed, and soils were examined. Potential factors

for varietal classification within and material type classification between samples was

determined to be impractical due to the strong confounding effect of moisture

dependence.

Sensor electrode topology was briefly touched on, raising interesting questions about

effects of geometry in dielectric sensors. The effect of material presentation was also

evaluated for both static and flowing samples. Using continuously flowing samples,

several varieties of corn were tested to evaluate existing density independent moisture

functions and density functions. The results verified the effectiveness of many functions

previously only studied in the microwave range for radio frequency instruments. In

addition, a new density prediction function was discovered to have significantly better

performance at radio frequencies.

iv

Table of Contents List of Tables ..................................................................................................................... vi List of Figures ................................................................................................................... vii Introduction......................................................................................................................... 1Background......................................................................................................................... 1

Complex Permittivity...................................................................................................... 2Polarization ..................................................................................................................... 2Frequency Dependence................................................................................................... 3Lumped Element Model ................................................................................................. 5Basic Dielectric Properties of Grain ............................................................................... 7Conductivity Effects ....................................................................................................... 8Dielectric Mixtures ......................................................................................................... 9Density Dependence ..................................................................................................... 10Hydrogen Bonding and Temperature Dependence....................................................... 11Instrumentation for Dielectric Measurement ................................................................ 14

Material Classification Studies ......................................................................................... 17Objectives ..................................................................................................................... 17Materials and Methods.................................................................................................. 17

Materials Tested........................................................................................................ 17Apparatus .................................................................................................................. 17

Observations ................................................................................................................. 21Linearity and Known Materials ................................................................................ 21Materials ................................................................................................................... 21

Data and Analysis ......................................................................................................... 22Constant Dielectrics .................................................................................................. 22Flat Plate Depth ........................................................................................................ 24Static versus Flowing Samples ................................................................................. 26Fertilizer.................................................................................................................... 27Soil ............................................................................................................................ 29Feed Stuffs and Grains.............................................................................................. 34Pattern Recognition................................................................................................... 38Moisture Dependence ............................................................................................... 40

Conclusions................................................................................................................... 43Flowing Grain Studies ...................................................................................................... 45

Objectives ..................................................................................................................... 45Materials and Methods.................................................................................................. 46

Grains tested ............................................................................................................. 46Apparatus .................................................................................................................. 47Sampling methods..................................................................................................... 50

Data and Analysis ......................................................................................................... 50Unprocessed Data ..................................................................................................... 50Differences Between FT and FP Sample Cells......................................................... 52Moisture Dependence ............................................................................................... 54Density Correction and Density Independence Methods ......................................... 56

v

Temperature Dependence ......................................................................................... 66Density Dependence ................................................................................................. 68

Conclusions................................................................................................................... 70References......................................................................................................................... 73

vi

List of Tables Table 1: Summary of basic soil materials and their dielectric constant at a frequency of

3200kHz.................................................................................................................... 30Table 2: Feed ingredients with response at 3.125kHz and 200kHz.................................. 36Table 3: Moisture values for corn, soy, and wheat. .......................................................... 42Table 4: Regression of parameters with contribution to moisture.................................... 43Table 5: Fitting parameters for simple linear regression (Equations 26 and 27) of

moisture against permittivity. ................................................................................... 56Table 6: Comparison of calibration error for several density terms to moisture and

permittivity regressions............................................................................................. 59Table 7: SEC results of function moisture prediction for FT and FP sensor cells...... 66Table 8: Temperature coefficients and their significance................................................. 67Table 9: SEC of various density regression models. ........................................................ 70

vii

List of Figures

Figure 1: Debye equation results for relative dielectric constant and loss. ........................ 4Figure 2: Analogous RC circuit for polarized molecular rotor in solid material................ 5Figure 3: Dielectric constant (a) and loss factor (b) measured over frequency and

moisture for hard red winter wheat (Nelson, 1981).................................................... 8Figure 4: Liquid water dielectric constant and dielectric loss at 0°C and 50°C (Funk,

2001). ........................................................................................................................ 14Figure 5: Schematic representation of commercially available sensor’s analog circuitry.

References in this figure: 1, 2: Microprocessor controlled direct digital synthesis oscillators; 3: Transmitter buffer amplifier; 4: Sensing chamber; 5, 6, 7: Receiver amplifier, bias and reference; 8: Analog multiplier; 9: Filter (Greer, 2002). ........... 18

Figure 6: FT Sensor Cell Dimensions............................................................................... 19Figure 7: FP Sensor Surface Dimensions and Electrode Configuration........................... 20Figure 8: Sensor instrumentation, including FT sample cell and user interface connected

to PC running LabView Software............................................................................. 21Figure 9: Variations in open air due to plastic liner (a) of dielectric constant and (b) loss

factor. ........................................................................................................................ 23Figure 10: Linear dielectrics evaluated with packing density variations observed (a) for

dielectric constant and (b) loss factor of glass beads in corn oil. ............................. 24Figure 11: Depth effect on measure of dielectric constant with FP sensor cell................ 25Figure 12: Boxplot of pooled static sample measurement of relative dielectric constant

compared to flowing sampling for (a) soybeans and (b) calcium phosphate at 3200kHz.................................................................................................................... 26

Figure 13: Initial fertilizer granule size distribution over six sieves. ............................... 28Figure 14: Response of dielectric constant in ground fertilizer........................................ 29Figure 15: Dielectric of common soil components and their dielectric constants............ 31Figure 16: Dielectric constant measured for silty loam soil (Hubbard) with added sand. 32Figure 17: Dielectrics constants for silty loam soil (other) when mixed with varying

fractions of sand........................................................................................................ 33Figure 18: Feed ingredients' dielectric constant response for (a) linear and (b) nonlinear

materials.................................................................................................................... 35Figure 19: Dielectric response of varieties of corn........................................................... 37Figure 20: (a) Wheat and (b) Soybean dielectric response among multiple varieties. ..... 38Figure 21: Best discrimination axes using Fisher's criterion. ........................................... 40Figure 22: Schematic Diagram of Pneumatic Grain Conveyor and Sampling System. ... 48Figure 23: Measured Permittivities of Corn by Sensor Type and Frequency; (a) Dielectric

Constant for FT Cell; (b) Dielectric Loss Factor for FT Cell; (c) Dielectric Constant for FP Cell; (d) Dielectric Loss Factor for FP Cell................................................... 52

Figure 24: Permittivity measurement nonlinearities by frequency and moisture; (a) Dielectric constant differences; (b) Dielectric loss factor differences...................... 54

Figure 25: Linear regressions on and predicting moisture; (a) Dielectric constant at 10kHz; (b) Dielectric loss factor at 160kHz. ............................................................ 55

Figure 26: ASABE predicted versus measured relative dielectric constant. .................... 57

viii

Figure 27: Landau and Lifshitz, Looyenga density correction improves overall fit of dielectric constant to moisture. ................................................................................. 58

Figure 28: Bulk density of grain shrunk for linear regression moisture predictor. .......... 60Figure 29: Contours of SEC for moisture prediction based on function; by frequency

and dielectric constant or loss factor......................................................................... 62Figure 30: Meyer & Schilz function for predicting moisture independent of density...... 63Figure 31: Complex plane plot of permittivity divided by density................................... 64Figure 32: values for function (Equation 38). ........................................................ 65Figure 33: Results of function moisture prediction..................................................... 66Figure 34: Temperature variations across all grain samples............................................. 68

ix

Disclaimer Reference herein to any specific commercial products, process, or service by trade name,

trademark, manufacturer, or otherwise, does not necessarily constitute or imply its

endorsement, recommendation, or favoring by the University of Minnesota nor the

author. The views and opinions of authors expressed herein do not necessarily state or

reflect those of the University of Minnesota, and shall not be used for advertising or

product endorsement purposes.

1

Introduction The instrumentation of agricultural systems has been an area of research interest

for many decades. In particular, study of the physical properties of products applied to

and harvested from fields in production agriculture has proven to be an enticing and

fruitful area of research. Grain is bought and sold on the basis of its moisture content and

density. Instruments that seek to measure those properties more accurately, with better

reliability, and more expediently have been developed over the past decades and have

received regulatory approval for trade. However, despite improving and expediting the

commercial handling of grain, these devices rely on undersized samplings of a much

larger volume of product (on the order of 25ppm). On-line sensors which measure a

significantly larger proportion of the product in real-time have started to see application.

One such commercially available instrument was developed to sense moisture and

density of whole kernel corn (Greer, 2002). This study focuses on the efficacy of real

time density and moisture sensors and examines applications for a variety of agricultural

material.

Background Dielectric materials provide an interesting media for electric field interactions.

These interactions have been studied intensely over the past century leading to a wide

range of applications. In particular, dielectric interactions have been studied for the

purposes of developing instrumentation for measurement of granular solids. The

following review identifies the underlying principles behind these types of measurements

and summarizes relevant literature in the field.

2

Complex Permittivity

Complex permittivity is the central property among examination of dielectrics.

This parameter indicates the ability of a given material to store energy imparted by an

electric field as well as its efficiency in storing the energy. Permittivity ( ) can be

expressed as a function of the permittivity of free space, . This quantity is known as

relative permittivity:

(1)

The relative complex permittivity (

€

εr∗) can then be expressed as:

€

εr∗ = ′ ε r − j ′ ′ ε r

(2)

The two terms of the complex permittivity are represented by the dielectric constant ,

which is the ability of a material to elastically store energy from an electric field, and the

dielectric loss factor , electric field energy dissipated by the material. These two terms

can also define the loss tangent:

(3)

which has been shown to be a useful measure to remove permittivity’s dependence on

density (Trabelsi et al., 1998).

Polarization

There are several mechanisms for storing energy in a dielectric material based on

polarization of individual atoms and molecules by the presence of an electric field.

Mechanisms include electronic polarization, occurring through the deformation of the

3

electron cloud surrounding individual atoms, and rotational polarization resulting when

polar molecules are reoriented by an electric field (Griffiths, 1981; Von Hippel, 1954).

Most study of dielectric materials focuses on molecular polar dipoles which can

have relatively large and distinctive dipole moments. A dipole’s polarity is measured in

Debyes (C m) indicating the strength of a charge and what distance it is displaced. In

particular, water, which has a 104 degree angle between its hydrogen atoms, has a

particularly strong moment of 1.84 Debyes ( C m).

Frequency Dependence

The complex permittivity of dielectrics is a frequency dependent property. Debye

(1929) found that for materials with a single relaxation method, the complex permittivity

of a material could be represented as a function of the response dielectric constant at low

frequencies ( ), at high frequencies ( ), a relaxation time constant ( ), and the

frequency ( ). The result, known as the Debye equation:

(4)

can be separated out into the real (5) and imaginary (6) terms, dielectric constant and

loss. (Both and are assumed to be real.)

(5)

(6)

4

!

!

1 10 100 1000 10000

0.0

0.2

0.4

0.6

0.8

1.0

Debye Results, Permittivity Normalized to

Frequency (Hz), !

Norm

aliz

ed R

ela

tive P

erm

ittivity,

"

r' &

" r

''

"r = 1

"r' : dielectric constant"r'' : dielectric loss

Figure 1: Debye equation results for relative dielectric constant and loss.

Figure 1 shows a normalized graph of the dielectric constant and loss factor as a

function of frequency for a material with a single relaxation method (e.g. molecular

dipole polarization). The behavior of the complex permittivity at its frequency limits

gives a good indication to the general behavior of dielectric relaxations. A maximum

permittivity will be obtained at the static limit (

€

ω = 0Hz). As the frequency rises, a

monotonic decrease in dielectric constant is observed until the high frequency limit

5

(

€

ω →∞) is reached. For the dielectric loss, a maximum, located at the midpoint between

static and high frequency dielectric constants, is achieved when the relaxation frequency

and the relaxation constant are equal.

Lumped Element Model

The Debye equation can be derived from the electrical response of an ideal RC

circuit, in which two capacitors are wired in parallel, one with an additional series

resistance. Von Hippel states that this approximation is appropriate due to the

dominating friction polar molecules experience in a solid material that allows the

simplification of the resonator model (LRC) to the RC circuit in Figure 2 with impedance

(Von Hippel, 1954):

€

Z = jωC1 +1

R2 +1

jωC2

−1

(7)

Figure 2: Analogous RC circuit for polarized molecular rotor in solid material.

6

If the capacitor is charged to a voltage and allowed to discharge, the

following response is observed over time:

€

V2 =V0e− tR2C2

(8)

The discharge time constant can be defined as . Given a parallel plate chamber

with open air capacitance , and impedance

€

Z =1 jωε∗C0 the impedances in Figure 2,

yields a permittivity of:

(9)

When the static and high frequency cases are examined, the analog between the

RC circuit and Debye’s model become apparent. For the high frequency limit the

permittivity becomes:

€

ε∞ =C1C0

(10)

and for the lower static limit (

€

ω = 0Hz) it is:

€

εS =C1C0

+C2

C0 (11)

giving a generalized form of:

(12)

This analog can be used to build more complex cases and allows for the approximation of

the behavior of a particular instrument.

7

Basic Dielectric Properties of Grain

Dielectric based measurement of moisture in grains has been used for nearly 100

years with evidence in patent filings from as early as 1929 (Heppenstall, 1929). Nearly

all of the work characterizing the quantitative dielectric properties of granular media has

occurred in the last 50 years. The vast majority of study has been on agricultural

materials, specifically grains and oilseeds with the goals of improving quality and

automation in agricultural processes (Nelson, 1981; Nelson, 2006). Most of this research

has focused on wheat and corn, with soybeans and other small grains studied to a lesser

extent. In studies where alternating current based instrumentation was used, the

frequency of measurement ranged from 250Hz to more than 12GHz. Moistures studied

were dependent on seed type and ranged from 2% wet basis moisture to more than 50%.

Over these ranges of frequency and moisture some generalizations about the dielectric

properties have been made. Increasing moisture in tested seeds resulted in monotonically

increasing dielectric constants ( ). These studies also indicated that

€

′ ε r either remained

constant or decreased with increasing measurement frequency. The correlation between

the dielectric loss factor ( ) and either moisture or frequency could not be generalized.

Figure 3 illustrates the frequency and moisture dependence for both dielectric constant

and loss factors over ranges of each for hard red winter wheat (ASABE, 2005). Over the

span of research, numerous studies cite several reasons for the irregular behavior of the

dielectric loss factor (Nelson, 1981; Funk et al., 2007). The most recent findings indicate

that the dielectric loss’ large values and steep slopes come not from dielectric relaxation

and dispersion as discussed above (polarization) which has been attributed to water

bound within the grains. Rather, Funk states that these effects are due to conductivity.

8

!

!

1e+02 1e+04 1e+06 1e+08 1e+10

510

15

20

25

Dielectric Constant in Wheat Over Moisture and Frequency

Ploted as Contours

Frequency (Hz), f

Mois

ture

Conte

nt (%

), %

M

!r': Dielectric Constant

500

300

200

100

50

30

20

10

7 5 4.5 4 3.5 3

2.5

2.2

2.1

(a)

!

!

1e+02 1e+04 1e+06 1e+08 1e+10

510

15

20

25

Dielectric Loss in Wheat Over Moisture and Frequency

Ploted as Contours

Frequency (Hz), f

Mois

ture

Conte

nt (%

), %

M

!r'': Dielectric Loss

400

300

200

100

50

30

20

10

5

3

2

1

0.7

0.5 0.4

0.3 0.2

0.15

0.1

0.1

0.15

0.2

0.3

0.4

0.5

0.7

(b)

Figure 3: Dielectric constant (a) and loss factor (b) measured over frequency and moisture for hard red winter wheat (Nelson, 1981). Conductivity Effects

Grimnes and Martinsen (2000) explain these effects as types of interfacial

polarization, that is, a collection of charge at boundaries within a measured sample. A

parallel-plate cell filled with a sample material and pulsed with alternating current

illustrates the simple case of electrode polarization. During each half cycle of sample

excitation, the electric field will create a charge carrier build up at the electrode’s

interface given the right conditions. One of these conditions is the relative resistance

between the sample cell electrodes and the sample material (contact resistance) and the

internal resistance of the sample material. If the contact resistance is large relative to the

internal resistance, charge carriers will migrate. As the electric field oscillation

frequency becomes very low (relative to the time it takes these charge carriers to move),

many charge carriers can accumulate at the electrodes. This charge movement appears as

9

an increase in permittivity despite having no link to the physical dielectric values of the

material being examined.

More complex are Maxwell-Wegner relaxations in dielectrics. In granular media,

each boundary between granules can become an electrical interfacial boundary (as above)

with varying boundary resistances due to the non-uniformity of most samples. Maxwell-

Wegner relaxation exhibits behavior similar to the Debye result (see Figure 3) where the

contribution to the dielectric constant decreases with increasing frequency. The dielectric

loss factor is also maximized where the dielectric constant is changing at the greatest rate,

going to zero at very low and very high frequencies. Funk concludes that conductivity

effects are particularly difficult to model due to the complexity of interactions within

granular materials and the effects’ large moisture dependent variations (Funk et al.,

2007).

Dielectric Mixtures

Dielectric measurements of single granules have obtained dielectric constant and

loss factor properties for a number of materials (Lawrence and Nelson, 2000; Nelson et

al., 1992). Extrapolating the single granule measurements, studies have modeled the

macroscopic behavior observed in measurements of granular media in bulk (Nelson,

2001; Hilhorst et al., 2000; Nelson, 2005). Most frequently the mixing is done in air, but

other studies have examined individual granule degradation by modeling multiple ground

fractions in addition to the whole material and air (Al-Mahasneh et al., 2001). Nelson

(2001, 2005) has shown repeatedly that the best models are the complex refractive index

mixture equation:

10

(13)

and the Landau and Lifshitz, Looyenga equation:

(14)

where , and are the complex dielectric constants of the mixture, the first and the

second materials, and and are the respective volume fractions. It has been shown

that the error performance of the Landau and Lifshitz, Looyenga equation is superior.

Nelson also suggested a simplification for the special case of an air-particle mixture, (the

typical case) which allows density corrections of permittivities to be made based on a

known permittivity and density pair (Nelson, 2005). The extrapolated complex dielectric

constant for an air-particle mixture can be represented by:

(15)

where is the known complex dielectric constant with density and is the

predicted complex dielectric constant at the new density .

Density Dependence

Much effort has gone into attempts at either removing the effect of density on the

correlation between complex permittivity and moisture or removing moisture’s effect on

the correlation between complex permittivity and density (Funk et al., 2007; Lawrence

and Nelson, 2000; Sacilik et al., 2007; Kraszewski et al., 2000; Trabelsi et al., 2001b).

Most recently the Landau and Lifshitz, Looyenga mixture equations have been

implemented by Funk as part of a unified moisture algorithm for sensing grain moisture

11

(Funk et al., 2007). Trabelsi developed another density independence model utilizing the

relationship between attenuation and phase shift at microwave frequencies (Trabelsi et

al., 1998; Trabelsi et al., 2001b; Trabelsi et al., 1999a). This equation ultimately yields a

moisture calibration expressed as a function of dielectric constant and loss factor:

(16)

where is the frequency dependent coefficient, determined by the slope of the plot

against . Ultimately, development of fitting algorithms for density correction

and determination continues to be an area of active research due to calibrations that are

too restrictive and do not generalize well.

Hydrogen Bonding and Temperature Dependence

In addition to density dependence, research has shown that the complex dielectric

constant depends on temperature at which a material is measured. Funk cites several

authors and develops a framework for understanding this behavior at a molecular level

(Funk, 2001). This framework depends on the concept of free and bound water. Many

authors have discussed the concept of free and bound water. The BET model defines

bound water as molecules where hydrogen bonding has been established between the

water and a polar site on the host material. Frequently carbohydrates and proteins

provide these sites in grains. This type of binding is also referred to as monolayer water;

the water molecules no longer have the freedom to create a lattice structure when cooled

below 0°C. In contrast, free water continues to freeze at 0°C, filling capillary spaces of

the material and continuing to allow for ionic conduction as it still functions as a solvent.

12

A further extension of the BET model involves decreased strength in binding forces for

water molecules beyond the first layer (monolayer) leading to a range of binding energies

for varying saturations of water within a material. These ranging binding energies are a

key driver in dielectric behavior of materials with significant fractions of water.

A quantitative study of water adsorption into grain gives credence to this model

(Trabelsi and Nelson, 2007). Hilhorst developed a relationship between relaxation

frequency and the required change in Gibbs free energy (Hilhorst, 1998). A further

extension of kinetic rate theory indicates that this relation can be quantized by correlating

the relaxation frequency ( ) to the probability of breaking a hydrogen bond that

restrains a water molecule during a single relaxation period ( ) (Funk, 2001).

The relationship is:

(17)

where is the change in Gibbs free energy, is Planck’s constant,

€

k is Boltzmann’s

constant, is the temperature in Kelvin, and is the gas constant. The reforming of

these bonds occurs very rapidly (~0.1ps) relative to most instrumentation (Kraszewski,

1996). This indicates that the relaxation time for water is driven primarily by molecules

waiting for their bonding energy to be overcome. Further derivation by Hilhorst shows

that only the portion of Gibbs free energy due to the molar activation enthalpy need be

considered (Hilhorst, 1998). That is . Continued development of this

relationship yields a relaxation frequency of a bound species of water, to be

proportional to the relaxation frequency of free water, . That is:

13

(18)

where (the molar activation enthalpy of free water) can be estimated to be

20.5kJ/mol and to be 17GHz. A lower bound to the relaxation frequency of 10kHz

can be determined by substituting the empirically determined value of 55kJ/mol for the

activation enthalpy of ice. Hence, hydrogen bonding plays a significant role in the exact

relaxation frequencies and thus the dielectric constants of materials with significant

fractions of water. Through this relation, temperature will also affect the dielectric

constant by increasing the relaxation frequency over increasing temperature. This effect

is mitigated by the increasing disorder of a system at higher temperatures and under

certain circumstances causes a decrease in the dielectric constant. These effects are

illustrated by Funk in Figure 4. Temperature dependence is primarily influenced by the

excitation frequency’s proximity to the relaxation frequency. Near the relaxation

frequency where the dielectric loss is significant, the effect of temperature is positively

correlated to the complex permittivity. Elsewhere, the effect is generally negatively

correlated. Research has confirmed these generalizations (Funk, 2001; Funk et al., 2007;

Trabelsi and Nelson, 2004).

14

!

!

1e+09 1e+10 1e+11 1e+12 1e+13

020

40

60

80

100

Liquid Water Dielectric Response

Frequency (Hz), f

Rela

tive

Die

lectr

ic C

onsta

nt and L

oss, ! r

' &

! r

''

!' at 0C

!' at 50C

!'' at 0C

!'' at 50C

Figure 4: Liquid water dielectric constant and dielectric loss at 0°C and 50°C (Funk, 2001). Instrumentation for Dielectric Measurement

Many sources discuss the implementation of devices designed to measure the

complex permittivity of materials (Nelson, 2006; Funk et al., 2007; Lawrence and

Nelson, 2000; Kraszewski et al., 2000; Trabelsi et al., 2001b; Nelson and Bartley, 2000;

Nelson, 1999; Trabelsi et al., 2001a; Nelson, 1992). Such devices have been designed to

15

measure properties of single granules of seeds as well as measurement of material in

bulk.

Two approaches have been used throughout the research: an impedance technique

based on the measure of relative capacitance and wave propagation measurement. The

classic example of the former is a test cell designed in the form of a parallel plate

capacitor with an initial dielectric of air. The measurement is completed when a sample

material replaces the air in the test cell and a change in capacitance is recorded. This

technique saw formative development from Nelson with the creation of a Q-meter that

quantified much of the earliest grain dielectric measurements (Nelson, 1999). The

complex dielectric constant is a simple ratio between the complex capacitance of the

filled test cell and the air filled (empty) test cell. Any additional contributions to the

capacitance of the air filled test cell, easily measured when empty, must be subtracted

from all measurements. Environmental factors like humidity should be controlled as they

can slightly alter the measurement of the air filled test cell.

The measurement of dielectric properties by wave propagation looks at phase

shift, attenuation and/or reflection of electromagnetic waves as they move through a

sample either in free space or within a section of transmission line. This technique relies

on the relation between the complex dielectric constant and the wave propagation

constant:

(19)

where is the attenuation constant, is the phase constant, is the free space

propagation constant, and is the complex dielectric constant. Transmission ( ) and

16

reflection ( ) measures, typically done with the use of a network analyzer, can be related

back to by:

(20)

and

(21)

Care must be taken to consider all possible boundaries and reflections within the test

system. Once a signal graph is determined, can be calculated from and (Pozar,

1990).

Numerous patents and reviews indicate the function and effectiveness of various

designs (Funk, 2001; Greer, 2002; Nelson, 2006; Lawrence and Nelson, 2000). Nelson

notes that nearly all commercially available sensors utilizing the RF dielectric/impedance

method use frequencies in the range of 1-20MHz (Nelson et al., 2000). More recent

technological developments have enabled the cost effective production of VHF and

microwave frequency sensors.

Research agrees that correction for the confounding factors of density and

temperature must be accounted for in the design and operation of instrumentation.

Equally important, research has shown that care must be taken in selection and fitting of

calibrations to correlate moisture and instrument signals.

17

Material Classification Studies Objectives

The examined instrument measures complex permittivity in grains and is designed

to distinguish moisture content and density differences. The objective of this study is to

evaluate potential uses for the instrument in granular materials. This goal includes

verifying moisture and density measurement abilities, distinguishing between different

materials, and classification by chemical composition.

Several experiments were conducted to determine instrument behavior. A series

of experiments were conducted to evaluate the basic operation and behavior of the sensor.

A second set of experiments were conducted to estimate material properties and their

relationship to the sensor. A final experiment was conducted to assess the confounding

physical properties of moisture, density, and temperature acting on the instrument.

Materials and Methods

MaterialsTestedThe major categories of materials evaluated included: ground and powdered feed

ingredients, whole grains, soils, and granular fertilizer. In these trials, moistures were not

controlled. Materials were allowed to equilibrate to ambient conditions (temperature and

humidity), which were then held constant for that group of materials.

ApparatusThe instrument utilized in these experiments is a shunt mode capacitive

measurement device (Greer, 2002). The sensor utilizes a microprocessor to control two

direct digital synthesis chips. The microprocessor initiates a sinusoidal signal to a

transmitting electrode in the sensor measurement chamber. At the receiver electrode, a

18

virtual ground amplifier biases and references the admitted signal. An analog multiplier

synchronously demodulates the received signal with a second sinusoid. The second

sinusoid alternates between in-phase and 90° out-of-phase, which allows the filtered

demodulated signal to represent either capacitance or dielectric loss. Figure 5 shows a

schematic representation of this function.

!"#$%&'

"%()*%+

,-./0&''

1%2+3(

4-#56!7

8

9

:

;

<

=

>?

Figure 5: Schematic representation of commercially available sensor’s analog circuitry. References in this figure: 1, 2: Microprocessor controlled direct digital synthesis oscillators; 3: Transmitter buffer amplifier; 4: Sensing chamber; 5, 6, 7: Receiver amplifier, bias and reference; 8: Analog multiplier; 9: Filter (Greer, 2002).

One configuration of this instrument, shown in Figure 6, utilizes a parallel plate

capacitance chamber allowing grains to flow through the sampling cell. This sensing

chamber will be hereafter referred to by its manufacturer part number: FT. The FT

permits grain to flow through for continuous monitoring. For the purposes of laboratory

evaluation of the instrument, a slide gate interrupts material flow, allowing the sensor

chamber to fill with a static sample. The FT sensor chamber measures 12.70 cm (5.00

in.) wide by 17.78 cm (7.00 in.) tall, with a 5.08 cm (2.00 in.) space between excitation

and sensing electrodes (Figure 6). The electrode plates are copper clad FR-4 printed

19

circuit board with 1.016 mm (0.040 in.) ceramic plating, measuring 12.70 cm (5.00 in.)

wide by 15.24 cm (6.00 in.) tall. The design of the parallel plate chamber uses the entire

transmit plate for a transmit electrode. The sensor uses a 6.35 (2.50 in.) by 8.89 cm (3.50

in.) portion of the receive plate for the receive electrode, with the remainder functioning

as a virtual ground.

Figure 6: FT Sensor Cell Dimensions.

An alternate sensor chamber, part number FP utilizes a flat plate configuration.

This alternate electrode configuration implements excitation and sensing electrodes on a

copper clad FR-4 printed circuit board with 1.016 mm (0.040 in.) ceramic plating.

However, this design places the electrodes side by side, separated by an electrode tied to

the device’s ground. The total size of the FP sensor is 12.70 cm (5.00 in.) wide by

20

17.78 cm (7.00 in.) long. An illustration of the FP electrode configuration is shown in

Figure 7.

Figure 7: FP Sensor Surface Dimensions and Electrode Configuration.

The sensing instrumentation records capacitance and dielectric loss data for frequencies

ranging from 3.125kHz to 6.4MHz by octaves. The instrument also records temperature

from probes in the sample cell and on the circuit board. The sensor stores this data in a

user interface that also provides calibration function (Rabbit Semiconductor OP7100).

An RS-232 link between the user interface and a personal computer running a custom

LabView software instrument allows logging of the sensor data (Labview, 1996). Figure

8 illustrates the devices used to generate and record capacitance and dielectric loss data.

21

Figure 8: Sensor instrumentation, including FT sample cell and user interface connected to PC running LabView Software. Observations

LinearityandKnownMaterialsIn order to better understand sensor behavior and assure linearity, tests using

some frequency constant dielectrics were conducted. If a material of known dielectric

strength could be examined, then a true dielectric value could be assigned to any material

examined in the instrument thereafter. In the context of examining physical effects on

the sensor, the FP sensor cell was also examined to provide information about how depth

of material affected the sensor’s reading and to put the FP sensor readings in context with

that of the FT sensor.

MaterialsFertilizer was examined to determine if a measure of the granular size distribution

could be accurately and repeatably performed to predict granule size degradation. With

fertilizer, granular size is an essential piece of information for proper application. The

expectation was that as the fertilizer was broken down into smaller pieces, the amount of

air between granules would decrease and would increase the signal to the instrument.

22

Using the sensor, it was predicted that a correlation could be made between the signal and

the fertilizer’s physical state.

Soils were examined with the instrument to find whether a relationship existed

between soil type and the signal from the instrument. It was expected that each soil type

could be linked to a response from the sensor, but density and moisture were anticipated

to have a confounding affect.

Feed ingredients and whole grains were examined to determine if differences

between ingredients existed. The expectation in this case was that each ingredient and

whole grain would have independent dielectric characteristics based on moisture and

physical shape and size, but also on the chemical makeup of the tested sample. These

differences in the multi-frequency spectra would reveal a way to distinguish one material

from another. It was expected that each material could be associated with a certain

sensor response and that moisture and density could be correlated to the instrument’s

response. The ultimate goal would be using the instrument as a one-size-fits-all moisture

and density monitor and/or as a sentry in a grain processing facility.

Data and Analysis

ConstantDielectricsAs a starting point for experimentation for the multi-frequency, capacitive sensor

and FT sensor, samples with dielectrics which had limited frequency dependence were

examined. The FT sensing cell was lined with a plastic Ziploc bag to accommodate

liquid (corn oil) for this experiment. The plastic lining caused a very slight deviation in

23

comparison to air alone, but the effect was within the limits of the variation of the sensor

itself, and hence ignored. These results are shown in Figure 9.

!

!

5 10 20 50 100 200 500 1000 2000 5000

0.8

0.9

1.0

1.1

1.2

Dielectric Constant for Empty Sensor

Lined and Unlined

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

Empty Sensor

Lined with 0.04mm Bag

(a)

!

!

5 10 20 50 100 200 500 1000 2000 5000!

0.1

0!

0.0

50.0

00.0

50.1

0

Dielectric Loss Factor for Empty Sensor

Lined and Unlined

Frequency (kHz), f

Rela

tive

Die

lectr

ic L

oss, ! r

''

Empty Sensor

Lined with 0.04mm Bag

(b)

Figure 9: Variations in open air due to plastic liner (a) of dielectric constant and (b) loss factor.

A mixture of 2, 3, and 5 mm glass beads was added to the FT sensor's lined

cavity. Readings from the sensor were taken once just as the beads were added, then

again while the cavity was shaken to eliminate any bridging and poor packing of the

glass. The cavity was shaken until no further change in signal was observed. Similarly,

once the signal from the glass had stabilized, corn oil was added to the FT sensor's cavity.

Again, readings were taken at intervals until the signal from the instrument no longer

varied between measurements.

The signal from glass beads that filled the cavity to approximately 50% volume

(the rest of the volume being occupied by air), was slightly over half of that expected

from solid glass. When corn oil was added, increasing the volume occupied by the

24

dielectric to 100%, the observed capacitance reached an expected value for the mixture of

corn oil and glass. The measured response by the FT sensor is shown in Figure 10. The

instrument gave a reasonably flat response across all frequencies, as it should have for the

materials examined. Also, as expected, the measured loss factor was near zero for these

materials.

!

!

5 10 20 50 100 200 500 1000 2000 5000

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Dielectric Constant for

Glass Beads and Corn Oil

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

! ! ! ! ! ! ! ! ! ! ! !

! ! ! ! ! ! ! ! ! ! ! !

!!

! ! ! !! ! ! !

!!

! !

! ! ! ! ! ! ! !!

!

!

!

!

!

Air

Glass

Glass Packing

Glass Packing

Glass Packed

Oil

Oil Settling

Oil Settling

Oil Settling

Oil Settled

(a)

!

!

5 10 20 50 100 200 500 1000 2000 5000

!1.0

!0.5

0.0

0.5

1.0

Dielectric Loss Factor for

Glass Beads and Corn Oil

Frequency (kHz), f

Rela

tive

Die

lectr

ic L

oss, ! r

''

!

!

!! ! ! ! ! ! !

! !

!

!

!! ! ! ! ! ! !

! !

!

!

!

! !! ! !

!

!

!

!

!

!

!

! !! ! ! !

!!

!

!

!

!

!

Air

Glass

Glass Packing

Glass Packing

Glass Packed

Oil

Oil Settling

Oil Settling

Oil Settling

Oil Settled

(b)

Figure 10: Linear dielectrics evaluated with packing density variations observed (a) for dielectric constant and (b) loss factor of glass beads in corn oil.

FlatPlateDepthThe FT sensor cell’s configuration was a well-known physical arrangement. If

the material to be examined was between its two parallel plates, the instrument would

collect and display the relevant data. Fringe fields are minimized by the FT sensor’s

configuration. However, for the FP sensor configuration, fringe fields become relevant.

Further, with no defined sample cell (as in the case of the FT) the sample depth can be

varied. A simple experiment was designed to discover how different depths of sample

affected the data collected by the instrument.

25

The FP sensor was laid at the bottom of a tub and corn was placed in the tub

above the sensor at varying levels. In the following graphs, both measured capacitance

and loss were affected by the amount of grain present above the sensor face. As the

depth of the corn increased, the value read by the sensor for either capacitance or loss

asymptotically approached a value.

!

!

5 10 20 50 100 200 500 1000 5000

01

23

45

Dielectric Constant for Increasing Depths

Using FP Sensor Cell

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

! ! ! ! ! ! ! ! ! ! ! !

!

!

!!

!!

! ! ! ! ! !

!

!

!

!

!

!!

!!

! !

!

!

!

!

Empty Sensor

1" Corn

2" Corn

4" Corn

6" Corn

8" Corn

Figure 11: Depth effect on measure of dielectric constant with FP sensor cell.

It should be noted that the 15 and 20 cm (6 and 8 in.) samples did not continue

this trend, but instead decreased the reading of the instrument. Further experimentation

showed that this decrease was likely due to variations in the physical arrangement of the

kernels. (See notes on static versus flowing samples for another example.) Hence,

26

beyond the 10 cm (4 in.) range for typical samples of corn, the instrument was able to

observe no differences.

StaticversusFlowingSamplesWould static samples adequately approximate the dynamic samples seen in the

application of the FT sensor cell? If static samples could not be used, material would

have to be allowed to flow through the sensor, making sampling in the laboratory much

more difficult. This question was answered empirically.

Soybeans were obtained from the University of Minnesota's agronomy

department. Enough seeds of a particular lot were collected to allow them to flow

through the FT sensor cell with partial restriction while data from the instrument was

collected. Figure 12(a) shows an example of the flowing samples, compared to a typical

static sample of the same soybean lot.

!!!!!!!!!!

!!!!!

Static Samples Flowing Samples

2.3

52.4

02.4

5

Comparing Dielectric Constant in Soybeans at 3200 kHz

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

(a)! Outliers

!

Static Flowing

2.7

52.8

02.8

52.9

0

Comparing Dielectric Constant in Calcium Phosphate at 3200 kHz

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

(b)! Outliers

Figure 12: Boxplot of pooled static sample measurement of relative dielectric constant compared to flowing sampling for (a) soybeans and (b) calcium phosphate at 3200kHz.

27

The sensor repeated itself across all frequencies, showing that the flowing

samples fell within the bounds of the multiple static samples; in this case fifteen samples

were pooled to give a range for static sampling. The measured result of flowing soybeans

was slightly higher than the identical material measured at rest. A similar experiment

was done with calcium phosphate obtained from a local feed manufacturer. In this case,

flowing sampling resulted in a slightly lower measurement, shown in Figure 12(b). This

result may suggest that there is some bias from either bulk density or material geometry

that causes the calcium phosphate to measure lower when sampled while flowing and the

soybeans to measure higher. However, any bias is small compared to the sampling error.

An adequate method is therefore to approximate the flowing material sampling by

filling and emptying the sensor several times for each material. This avoids the logistical

problems of handling greater volumes of material. Collecting multiple data points allows

for approximation of the true mean better than single static samples.

FertilizerThe question was raised as to whether the instrument could be used to determine

fertilizer degradation. Theory behind capacitive sensing at kilohertz to low megahertz

frequencies dictates that water has the primary influence on dielectric strength, and with

density having a secondary affect. Since degraded fertilizer would be in smaller pieces,

the packing density will therefore increase and a noticeable increase in signal from the FT

sensor should be seen.

To test this hypothesis, a commercially available fertilizer was purchased. A

single grain size analysis of the un-degraded fertilizer was done and the results are shown

28

in Figure 13. The results of the sizing were consistent with standards for analyses of

other common granular materials (ASABE, 2008a).

!!

!

!

!

!

!

1 2 3 4 5 6

020

40

60

80

100

Fertilizer Particle Size Distribution, Unground

Particle Size, Smaller Than (mm)

Perc

enta

ge o

f P

art

icle

s in R

ange (

%)

!!

!

!

!

!!

Figure 13: Initial fertilizer granule size distribution over six sieves.

Three lots were created from the remaining material. Sample one was examined

with the sensor as it was, straight from the bag. A small roller mill was then used to

degrade samples two and three. Sample two was ground for one minute and sample three

for two minutes in the mill. In both cases, the roller mill degraded the fertilizer evenly,

without grinding all granules to a fine powder.

As can be seen in Figure 14, the performance of the instrument was more than

adequate to show a correlation between degradation of the fertilizer and the capacitive

and loss signals received at and above 200kHz. (Signals below this frequency exceeded

29

the instrument’s range and are therefore irrelevant, as evidenced by the plateau across the

5-150kHz range.) More study would be necessary to quantify the relationship and

remove the moisture dependence variable.

!

!

5 10 20 50 100 200 500 1000 5000

34

56

78

9

Dielectric Response of Degraded Fertilizer

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

Unground

1 minute grind

2 minute grind

Figure 14: Response of dielectric constant in ground fertilizer.

SoilAlong the same vein as the investigation into fertilizer degradation came the idea

that soil types could be identified by the tested instrument. A desired instrument would

be able to detect a five percent change in soil compositions. The various types of soils

seen throughout the region vary by their component size distribution. The major

component groups are sand, silt, and clay. Different combinations of these ingredients

30

were mixed with each other as well as with existing soils to show whether or not

differences could be seen between slightly dissimilar soils.

Table 1 shows a brief summary of the relative dielectric data for representative

soil components at 3200kHz. There is a wide range of variation between the different

ingredients (dielectric constants from 2.23 to off-scale). A complete graph of the entire

frequency range is shown in Figure 15. The soils’ dielectric constant decreases over

increasing instrument frequency. Note that several of the materials exceed the range of

the sensor between 5 and 100kHz. It is also noteworthy that the complex soils read lower

than any constituent ingredient. In samples examined, moisture was not controlled,

however all samples were equilibrated to the sampling environment prior to testing.

Table 1: Summary of basic soil materials and their dielectric constant at a frequency of 3200kHz.

31

!

!

5 10 20 50 100 200 500 1000 5000

24

68

Graph of Dielectric Constants for Soil Components

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

!

!

!! !

!

!

!

!

!

!

!

!

!

! ! ! ! !!

!

!

! !

! ! ! ! ! ! ! ! ! ! ! !

!

!

!

Clay

Silt

Dried Silt

Damp Silt

Sand (#2)

Sand (#7)

Silty Loam Soil (Hubbard)

Silty Loam Soil (Other)

Figure 15: Dielectric of common soil components and their dielectric constants.

A single mixture of sand was added to the silty loam soil (Hubbard) and

additional sand measurements were taken with the silty loam soil (Other) at rates of 5, 10,

20 and 40% (by volume). For the silty loam and sand mixes, the pure sand samples had

much larger measured capacitances than the combined samples. Depending on the size

of sand grains added to the silty loam, the signal changed accordingly. In the Hubbard

soil, the addition of sand caused a decrease across all frequencies. Figure 16 shows this

relationship.

32

!

!

5 10 20 50 100 200 500 1000 5000

2.5

3.0

3.5

4.0

4.5

Graph of Dielectric Constants

for Silty Loam Soil (Hubbard) with Added Sand

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'Silty Loam Soil (Hubbard)

Silty Loam Soil (Hubbard)/Sand Mix

Figure 16: Dielectric constant measured for silty loam soil (Hubbard) with added sand.

When sand was added to the silty loam soil (other) it generally increased the

signal. The most drastic change was seen with the coarse sand (#2, 0.5-1.0 mm), which

shifted the capacitance up across all frequencies as shown in Figure 17(b). The fine grain

sands had other effects on the capacitance. For the fine (#7, 125-250 µm) sand, the

capacitive values increased with the addition of the sand (Figure 17(c)). However, as

more was added, the lower frequencies saw a decrease in signal (to a point lower than the

original silty loam), and the upper frequencies stayed approximately the same.

33

!

!

5 20 100 500 2000

24

68

Frequency (kHz), f

Re

lative

Die

lectr

ic C

on

sta

nt,

! r

'

! ! ! ! ! ! ! ! ! ! ! !

!

!! ! ! ! ! !

!

!

! !

(a)

!

!

Silty Loam Soil (Other)

Sand (#2)

Sand (#7)

!

!

5 20 100 500 2000

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Frequency (kHz), f

Re

lative

Die

lectr

ic C

on

sta

nt,

! r

'

!

!

!

!

!

!

!

!!

! !

!

(b)! Silty Loam Soil (Other)

+5% Sand (#2)

+10% Sand (#2)

+20% Sand (#2)

!

!

5 20 100 500 2000

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Frequency (kHz), f

Re

lative

Die

lectr

ic C

on

sta

nt,

! r

'

!

!

!

!

!

!

!

!!

! !

!

!

!

!

!

!

!

!

!!

! !

!

!

!

!

!

!

!

!

!!

! !!

!

!!

!!

!

!!

! ! !!

(c)!

!

!

!

Silty Loam Soil (Other)

+10% Sand (#7)

+20% Sand (#7)

+40% Sand (#7)

!

!

5 20 100 500 2000

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Frequency (kHz), f

Re

lative

Die

lectr

ic C

on

sta

nt,

! r

'

!

!

!

!

!

!

!

!!

! !

!

(d)! Silty Loam Soil (Other)

+5% Sand (#2)/5% Sand (#4)

+Sand (#2)/Sand (#7)

+5% Sand (#4)/5% Sand (#7)

Graph of Dielectric Constants for Silty Loam Soil (Other) as Sand is Added

Figure 17: Dielectrics constants for silty loam soil (other) when mixed with varying fractions of sand.

Considering the original problem statement, can the instrument be used to detect

differences in soils at a five percent level? For certain elements in certain soils the sensor

does well. The best example is the addition of coarse sand to silty loam soil, where a five

34

percent addition was significant across all frequencies. Unfortunately, soils in practice

will have varying moisture contents. The problem then becomes having a sensor that can

measure larger capacitances and not be confounded by the variation in moisture contents.

Caveats aside, the experimental data showed promise that the instrument could be

calibrated to measure changes in soil composition.

FeedStuffsandGrainsA variety of ground meals and other feed ingredients were obtained to create a

reference spectra. The list of feed ingredients is shown in Table 2. Figure 18 depicts the

capacitive spectra observed by the instrument for each sample. It can be noted that the

granular compounds (salt and calcium carbonate) had a very flat response over the range

of frequencies and independent of dielectric constant. Linearity of response was judged

by residual variation on a linear regression. Non-linear models had a variation in

residuals of at least 10% of the relative dielectric and a noted “U” shaped residual

response over frequency.

35

!

!

5 10 20 50 100 200 500 1000 2000 5000

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Ground Meals ! Linear Response

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! !

! ! ! ! ! ! ! ! ! ! ! !

(a)!

!

!

alfalfa meal

bran

calcium carbonate

cereal fines

corn glutton meal

deproteinized whey

dried molasses

ground beet pulp

lactose

salt

soybean hulls

!

!

5 10 20 50 100 200 500 1000 2000 5000

23

45

67

8

Ground Meals ! Nonlinear response

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

!

!!

!! ! ! ! ! ! ! !

!

!

!

!

!

!

!

!!

! !!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!!

!! ! ! !

(b)

!

!

!

!

calcium phosphate

corn screenings

dried whey

ground corn

ground milo

ground oats

hi fat rice bran

linseed meal

red dog

sol u lac

soy hulls

soybean meal

steamed rolled oats

wheat midds

Figure 18: Feed ingredients' dielectric constant response for (a) linear and (b) nonlinear materials.

The instrument was equipped to obtain moisture and density values from corn. It

was reasoned then, that there may be additional data readily obtained from the sensor,

which corresponded to other physical parameters, including kernel shape, size, and even

nutritional value. Therefore, data from numerous varieties of several different grains was

collected. The four major components of this experiment included corn, soybeans,

wheat, and as previously discussed, ground meals and feed ingredients.

36

Table 2: Feed ingredients with response at 3.125kHz and 200kHz.

Figure 19 and Figure 20 illustrate each crop seed’s response by variety. For corn,

two varieties of hybrid seed were examined. One was a waxy corn with high oil content,

hybrid number N4342Wx from Syngenta Seeds. The other was a Bt variety, N4242Bt,

also from Syngenta. One lot of each grain was tested after being allowed to equilibrate to

ambient conditions. Each lot was sampled 10 times with 12 replicates. One standard

deviation from the average sample collected is shown as an error bar on each data point.

The two corn hybrids showed significant differences in their capacitive spectra as

observed by FT sensor cell.

37

!

!

5 10 20 50 100 200 500 1000 5000

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

Dielectric Response of Varieties of Corn

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

!

!

!

!

!

!

!

!

!!

!

!

! N4242Bt

N4342Wx

Figure 19: Dielectric response of varieties of corn.

24 varieties of wheat were examined with the instrument. All varieties of wheat

were obtained from the University of Minnesota Agronomy Department. As can be seen

from Figure 20(a), the variation between varieties was so small, variation within samples

made it difficult to differentiate the individual wheat samples using the capacitive

spectra.

A number of soybean varieties were also made available by the University of

Minnesota Agronomy Department. 15 different varieties of internally bred and

commercially available soybean seed were tested. The capacitive spectrum of the

soybeans was somewhat wider than that of wheat, but still too close for inter-varietal

differentiation. Figure 20(b) does illustrate that a few varieties stood out due to large or

38

small seed size. IA2050 and M97-206017 had seed sizes of approximately 25% less and

50% greater than the mean seed diameter of other varieties respectively. However, most

varieties filled in the space between.

!

!

1e+01 1e+02 1e+03 1e+04 1e+05

3.0

3.2

3.4

3.6

3.8

4.0

4.2

Dielectric Response of Varieties of Wheat

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

2375

BACUP

MN98223

MN98227

MN98229

MN98230

MN98284

MN98285

MN98294

MN98299

MN98329

MN98339

MN98344

MN98354

MN98365

MN98366

MN98367

MN98368

MN98369

MN98383

MN98386

MN98392

MN98399

VERDE

(a)

!

!

1e+01 1e+02 1e+03 1e+04 1e+05

2.3

2.4

2.5

2.6

2.7

2.8

Dielectric Response of Varieties of Soybeans

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

!

!

!

!

!

!

!

!

!

!!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!!

!

!

!

!

DANATTO

IA2050

KATO

LAMBERT

M97!204002

M97!204010

M97!205015

M97!205108

M97!205114

M97!206017

M97!2204016

Pioneer 9071

SGILS!70

TOYOPRO

Vinton 81

(b)

Figure 20: (a) Wheat and (b) Soybean dielectric response among multiple varieties.

PatternRecognitionNo clear path to inter-varietal identification of wheat and soy was found due to

the statistical insignificance of variations between varieties. Since inter-varietal

identifications could no be made, it was proposed that the sensor be used as a classifier to

make inter-material-type identifications. Again, the four major categories of

classification were deemed to be the seeds of corn, wheat, soybeans, and the general

category of feed ingredients and other ground meals.

Pattern recognition algorithms were determined to be an efficient way of

programming the sensor to be a classifier. The first step in using pattern recognition is to

determine what data is significant. Since the capacitances at all twelve frequencies of the

39

instrument were assumed to be meaningful, the most logical way to reduce the data set

was to create fourth order polynomials, which were frequency dependent. This set of

polynomials collapsed the twelve frequency points into five coefficients for each sample.

Using a technique called Fisher's criterion to create maximum separation between

points, several possible correlations of the samples to a two-dimensional coordinate

system were reached as shown in Figure 21 (Webb, 2002; Braun, 2003). The final step in

implementing pattern recognition was to determine a method to classify the points based

on where each point was in relation to one another. A commonly used classification

method is k-nearest neighbors.

Implementation of this pattern recognition scheme brought forth error rates of

below five percent on initial training sets. However, because concerns about the

confounding effects of moisture content were not closely examined in this experiment,

further data was not collected for this classifier. Instead an experiment to investigate

moisture dependence of the instrument was carried out.

40

!

!

!600 !500 !400 !300 !200 !100 0

!1.5

e!

11

!1.0

e!

11

!5.0

e!

12

0.0

e+

00

Fisher's Criterion, Best Discriminant Axes

Discriminant Axis (dimensionless)

Dis

cri

min

ant A

xis

(dim

ensio

nle

ss)

!

!

!

!

!

!

!

!

!

! W0: Soybeans

W1: Wheat

W2: Ground Meals

W3: Corn

Figure 21: Best discrimination axes using Fisher's criterion.

MoistureDependenceThe cumulative experiment in this segment of study was to look at several

different types of crop seeds and the effect moisture variation had on the instrument. The

objective was to use the data as a training algorithm for a classifier using pattern

recognition.

The experiment was set up as a randomized block. Moisture was controlled for,

but density was not. Three replicates of each of six moisture levels for each of the three

different seeds (corn, wheat and soy) were prepared. Samples needing to have moisture

added were re-wet using the standard procedure of adding distilled water, tumbling the

wetted grain for two hours and then placing it a sealed container just above 0°C for 72

41

hours. This allowed moisture to be fully absorbed into the seed and minimize any

unbound water or moisture gradients. Prior to sampling, the sealed bags of grain were

removed from the cooler and allowed to equilibrate to room temperature (22.5°C).

Samples were not large enough to accommodate sampling moving grain, so

simple static samples were taken. Through the instrument’s data acquisition, 10 samples

of each replicate were obtained. Once data had been gathered from the FT sensor cell,

samples were re-bagged to allow for oven moisture measurements. ASABE standard

S352.2 methods were used to obtain moistures for each of the 51 samples listed in Table

3 (ASABE, 2008b).

42

Table 3: Moisture values for corn, soy, and wheat.

When all of the data was collected, it was found that the data set was too small to

run a pattern recognition algorithm. From the data set, it was determined that the

differences between grains were not great enough to overcome the dominant relationships

between capacitive spectra and physical properties of moisture and density.

An analysis of the dependence of moisture on capacitive output from the instrument

follows in Table 4. Each of the capacitive values at frequencies 5 (50kHz), 8 (400kHz),

10 (1600kHz), and 11 (3200kHz) made significant contributions to the relationship

between moisture and capacitance (Oehlert and Bingham, 2000).

43

Table 4: Regression of parameters with contribution to moisture.

Any attempt to make other relationships out of the data set obtained in this

experiment resulted in poorly correlated functions. As a final result, the instrument did

well at sensing moisture in whole grains, but poorly at sensing other physical parameters

of the grain due to its strong primary dependence on water.

Conclusions

The assumption was made at the outset of this research that the commercially

available sensor could measure moisture and density effectively and independently of the

complex permittivity readings retrieved by the laboratory interface. However, this data

was not independent, but instead closely tied to the ability of the instrument to read

moisture and density. This incorrect assumption led to overlooking the acquisition of

crucial moisture and density data for all but a few of the many observational studies. The

effects of moisture and density confound the results of the remaining studies.

However, numerous qualitative results based on the behavior of the sensor

supplied useful information. The instrument examined gave a linear response to linear

44

dielectrics with relative complex permittivities within an expected range. Differences

between static samples and moving samples were compared in the FT sensor cell

showing that static samples could be used to approximate a dynamic sample. The FP

sensor cell configuration was evaluated and compared to the response from the FT sensor

cell. It was found that the depth of product at the FP sensor cell needed as little as 10 cm

(4 in.) for proper measurement.

Relationships between density and permittivity were found which could provide

the basis for future study. The degradation of granular fertilizer showed a clear

relationship between increasing permittivity and increasing density at constant moistures.

Differences in some soils at constant moistures were also shown to have a monotonic

relationship with permittivity. Variations due to moisture content in these materials were

not investigated at this time.

Feed ingredients and whole grains were found to be surprisingly similar in their

measured relative permittivities. The assumption was made that varietal differences

within individual grains would either overwhelm the correlation with moisture, or that

these differences would be insignificant. Through the use of pattern recognition

techniques, a classifier was trained on data from numerous varieties with reasonable

success at differentiating between grain types. However, moisture remained a

confounding variable. A final attempt to remove the effect of moisture only underscored

the strength of the relationship between moisture and measured permittivity. These

results provided the basis for additional study with grains whose moisture and density

could be well controlled.

45

Flowing Grain Studies

Objectives

Previous analysis of the commercially available instrument left questions about

the validity of the algorithms implemented in calculating moisture and density from

multiple measures of the dielectric constant and loss factor in grains and other materials.

In 2005, the manufacturer developed a replacement for the original sensor, hereafter

referred by its part number: A4MS. This revised device utilized the same FT and FP

sensing chambers, but had additional capabilities that addressed some of the problems

with the original instrument. The objective of studying this device was to evaluate

existing density independent functions published in the literature and by the inventor, and

to determine what level of accuracy while sensing both moisture and density in grain

could be determined (Trabelsi et al., 1998; Funk et al., 2007; Greer, 2005).

This study was designed to remove the variables of hand filling the instrument

and to look at bulk density variations. Additionally, the instrument allowed a much

greater dynamic range to prevent the clipping of high dielectric values as occurred in

initial studies. Multiple sensor sample cells were evaluated to test for differences in

measurement by grain presentation and sensor configuration.

The calibration algorithms for the original instrument were based on a limited

data set with most bulk density variations induced by packing density changes. The

literature maintains that packing density is only part of the density variation measured by

dielectric methods (Funk et al., 2007). Since packing density variations are difficult to

control, in this study multiple varieties of #2 yellow dent field corn were obtained from a

local grain producer's test plot yielding naturally induced changes in bulk density. To

46

control packing density fluctuations and avoid artificial bias, a continuous stream of grain

was allowed to flow through the instrument's test cell rather than taking static samples.

In the original instrument, many readings at mid-range frequencies for high-dielectric

samples were off-scale. An internally adjustable gain control was implemented in the

revised instrument. This control resulted in more usable data to evaluate over all

frequencies.

In initial experimentation, the FP configuration was subjected to a basic

evaluation. In this study, both FT and FP configurations were tested in tandem. This

allowed comparison between the two configurations to evaluate any advantages or

disadvantages inherent in either sample cell.

Numerous methods of correlating moisture to dielectric measurements have been

cited by the literature. This study will evaluate both density dependent and density

independent methods of instrument calibration to determine both the best accuracy and

the most robust methods of predicting moisture and density. New relationships between

density and moisture at kHz and low MHz relationships were sought to provide optimal

calibration for the instrument.

Materials and Methods

GrainstestedYellow #2 field corn was obtained from a local grower's variety test plot. This

allowed for a sampling of 16 varieties of grain ranging in bulk density from 0.70 to 0.77

g/cm3. Initial moisture contents of the corn ranged from 16.0% to 18.5% wet basis

moisture. The corn was prepped for experimentation by removing excess chaff and fines

47

by air separation. The removal was done shaking the grain on 4.76 mm wire mesh

grating with air blown across until most of the fines were removed. The corn was stored

at room temperature and allowed to air-dry in 27 kg paper grain sacks, two sacks per

grain type. During the experimentation, each bag was sampled and if moisture variation

between bags of the same grain type was significant, the separate lots of the same grain

were remixed and allowed to equilibrate.

Over the course of the experimentation the grain samples dried significantly. A

protocol for re-wetting grain developed at the University of Minnesota's Department of

Biosystems and Bioproducts Engineering was used to reconstitute the grain to desired

sample moistures. Lots of grain were tumbled at approximately 4 RPM in a 60 L axially

rotating drum (35.6 cm diameter x 66.0 cm length). Water was added two to three

percent by weight at a time and the resulting mixture was tumbled for two hours. When

the water was adsorbed, the grain was re-bagged, sealed and allowed to equilibrate for no

less than 72 hours at 10°C. Due to the size limitation of the 60 L wetting drum, each half

lot (13.5 kg) of grain was re-wetted individually rather than as a single sample. Several

cycles through the sampling apparatus mixed the lots thoroughly and differences between

the two lots of each sample were not observed.

ApparatusIn order to provide a continuous sample to the FP and FT sensor sample cells, a

pneumatic conveyor was constructed from 10 cm (4 in.) PVC piping. The grain was

conveyed using a blower fan (Hartzell Corporation Series 07) producing approximately

14.2 cubic meters per minute of airflow. A 19 L (5 gal) loading hopper filled this system

and allowed for approximately 6.8 kg of corn per minute to be continuously cycled

48

through the sensor test cells and returned to a buffer hopper above the sample cells where

it could gravity feed into the sensors below.

!"#$%&'()*

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/#)01*2'-#..%&

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Figure 22: Schematic Diagram of Pneumatic Grain Conveyor and Sampling System.

Figure 22 shows a schematic representation of the equipment. Each sample of

corn was allowed to cycle through the apparatus multiple times. Over the course of a 60

minute sampling period, the grain typically dried 0.5% due to air flow in the pneumatic

conveyor.

49

Two moisture sensor sample cells were connected in series with a control gate below the

lower sensor. The FT sensor was located above and the FP sensor was located below.

As in the earlier studies, the dimensions of the FT sample cell are given in Figure 6. The

electrodes of the sensors were copper on FR-4 fiberglass circuit board, protected by a

1.016 mm (0.040 in.) non-porous ceramic. For the FP sensor, the sample cell was

identical to the FT. Only the sensor electrode configuration was changed; both electrodes

were mounted in the same plane as shown in Figure 7. Grain flow was modulated by

attaching an electrically actuated vibrator to the control gate.

Data was collected from the two sensors using instrumentation attached to a

laptop running a custom LabView virtual instrument on Windows 2000 via a proprietary

protocol over an RS485 physical interface (National Instruments, 1996).

The internal workings of the new instrument functioned similarly to the previous

device. Pulse trains of sinusoids were sent in 12 octave steps between 10kHz and 20MHz

to an electrode adjacent to the grain sample. A second electrode sensed the attenuated

signal. Multiple instrumentation amplifiers fed this signal to an analog multiplier that

was used to compare to an in-phase and an out-of-phase version of the original signal.

These measurements were recorded directly by 10-bit analog to digital converters in the

circuitry and output via the aforementioned RS485 physical interface. The raw data was

stored in a tab-delimited file that could then be further analyzed.

Other factors automatically recorded by the instrumentation included a time

stamp, temperatures from a sample probe, and circuit board level temperature

measurement device, the RS485 sensor address, and the sensor sensitivity or gain setting.

50

SamplingmethodsGrain moisture levels and densities were measured multiple times during each

sampling period. The corn temperature was monitored continuously through the

instrumentation. The protocol established was to load the sample of grain (sample weight

ranging from 45 to 54 kg) into the pneumatic conveyor's lower hopper. Once a uniform

and controlled flow of approximately 2.3 kg per minute was established through the

sensing cells, 1.4 kg samples were collected from the lower sensor cell discharge for

analysis. Additional 1.4 kg samples were taken every twenty minutes. Each time a grain

sample was retrieved, the computer data acquisition system was flagged to denote exactly

when the sample was drawn to provide optimum correlation to the analytical values.

Moisture measurement calculated by the standard method for wet basis moisture

using a Blue-M model OV-475A-2 air-oven at 103°C for 72 hours (ASABE, 2008b).

Triplicate samples of 15 grams were weighed using an AND model FX-320 electronic

balance. Density measurement was performed by filling a Seedburo #204 dry quart cup

with corresponding filling funnel and striking off the excess grain. Cup weights were

measured with an OHAUS 800 series triple beam balance.

Data and Analysis

UnprocessedDataThe data recorded from the A4MS instrument was unprocessed in and out-of-

phase data for each frequency ( and respectively). Additionally, before

and after each sample the sensors were allowed to empty out and read only air, giving a

reference zero: and . To be of analytical use, the data was translated to

51

dielectric constant ( ) and loss factor ( ) values. Equations 22 and 23 illustrate the

conversion.

(22)

(23)

Figure 23 illustrates the measured dielectric constant and loss factors for the FT and FP

sample cells.

52

!

!

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!

!!!!

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!!!!

!!!

!!!!

! !!

!!!!

! !!

!!!!

!!

!!!!!!!!!!

!!!!!!

!!!!!

!!!!!!

3.125 12.5 50 200 800 3200

46

810

Dielectric Constant Measurements

FT Cell

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

(a)!

!

!

!!!

!

!

!

!!!

!

!!!!!

!!!!!!

!!!!!!

!!!!!!

!

!!!!!!

!

!!!!!!

!!!

!!!

3.125 12.5 50 200 800 3200

0.0

0.5

1.0

1.5

2.0

2.5

Dielectric Loss Factor Measurements

FT Cell

Frequency (kHz), f

Rela

tive

Die

lectr

ic L

oss F

acto

r, !

r''

(b)

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!

!!!!!!!

3.125 12.5 50 200 800 3200

34

56

78

910

Dielectric Constant Measurements

FP Cell

Frequency (kHz), f

Rela

tive

Die

lectr

ic C

onsta

nt, !

r'

(c)

!!

!!

!

!!!!!!

!!!!!!

!!!!!!

!!

!!!!!!!!

!

!!!!!!

!!

!

3.125 12.5 50 200 800 3200

!1.0

!0.5

0.0

0.5

1.0

1.5

2.0

Dielectric Loss Factor Measurements

FP Cell

Frequency (kHz), f

Rela

tive

Die

lectr

ic L

oss F

acto

r, !

r''(d)

Figure 23: Measured Permittivities of Corn by Sensor Type and Frequency; (a) Dielectric Constant for FT Cell; (b) Dielectric Loss Factor for FT Cell; (c) Dielectric Constant for FP Cell; (d) Dielectric Loss Factor for FP Cell.

DifferencesBetweenFTandFPSampleCellsDue to the physical differences between the sensor electrodes in the FT and FP

sample cells, the measured complex dielectric readings were significantly different. The

measured relative permittivity of the FP sample cell (sensor electrodes in single plane

configuration) was approximately double that of the FT sample cell (sensor electrodes in

53

parallel plate configuration). Equations 24 and 25 give capacitance estimates for the FT

and FP sensor cell topologies (FP sensor estimated by parallel wire configuration).

, (24, 25)

This result gave a slightly higher correction factor (0.58) than what was observed

experimentally (a factor of 0.50). The difference was ascribed to the rough physical

model used for the FP configuration and the experimentally observed correction was

used.

What was not immediately explained was the non-linearity with which the A4MS

instrument reported dielectric measurements between the two configurations. Figure 24

shows the differences between FT and FP sample cells. The non-linearity is particularly

pronounced in the lowest frequencies of the dielectric constant and there is a strong

moisture correlation to this effect. The topological differences between the FT and FP

sample cells do have bearing on the measurement of permittivity and should be noted,

particularly for the frequencies 10kHz and 20480kHz.

54

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10 50 100 500 1000 5000

!0.5

0.0

0.5

1.0

1.5

Frequency (kHz), f

Die

lectr

ic C

onsta

nt D

iffe

rence, ! r

'

(a)

!

Moisture > 17%

Moisture ~ 16.5%

Moisture ~ 16.0%

Moisture ~ 15.5%

Moisture ~ 15.0%

!

!

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10 50 100 500 1000 5000

0.0

0.5

1.0

1.5

Frequency (kHz), f

Die

lectr

ic L

oss F

acto

r D

iffe

rence, ! r

''

(b)

!

Moisture > 17%

Moisture ~ 16.5%

Moisture ~ 16.0%

Moisture ~ 15.5%

Moisture ~ 15.0%

Dielectric Constant and Loss Factor Differences Between FT & FP Cells

Figure 24: Permittivity measurement nonlinearities by frequency and moisture; (a) Dielectric constant differences; (b) Dielectric loss factor differences.

MoistureDependenceAs noted throughout the literature, the measure of dielectric constant is a well

known predictor of moisture content in a wide variety of grains. Therefore, a proper

beginning to analyze the effects would examine the models:

and (26, 27)

In addition to using Pearson’s Correlation Coefficient to evaluate performance of models,

the Standard Error of Calibration (SEC) is used:

(28)

Where is the number of samples, is the number of variables in the regression, and

is the difference between the value predicted by the regression and the value obtained

experimentally.

55

For a simple linear model, best moisture prediction performance was obtained by

the dielectric constant measurement at 10kHz with a SEC of 0.37% for the FT sample

cell. This is shown Figure 25(a). The FP sample cell responded with an SEC of

approximately six percent more over the entire frequency range. The dielectric loss

factor's performance as a predictor was similar and is illustrated in Figure 25(b), and

frequencies between 40kHz and 320kHz maintained SEC of less than 0.36%. Again, this

was the result of the FT sample cell. The FP sample cell had larger prediction intervals,

but much closer (two percent) than the dielectric constant predictor.

!

!

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!

6 7 8 9 10 11

16

17

18

19

Relative Dielectric Constant, !r'

Measure

d M

ois

ture

Conte

nt (%

), %

M

(a)

R2 = 0.84

!

!

!

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!

0.4 0.6 0.8 1.0 1.2 1.4

16

17

18

19

Relative Dielectric Loss Factor, !r''

Measure

d M

ois

ture

Conte

nt (%

), %

M

R2 = 0.86

(b)

Moisture predicted by relative dielectric constant and loss factor, !r' at 10kHz and !r'' at 160kHz

Figure 25: Linear regressions on and predicting moisture; (a) Dielectric constant at 10kHz; (b) Dielectric loss factor at 160kHz.

A complete table of the fit coefficients and expected error is shown in Table 5.

The additional factors of density and temperature are known variables entering into the

dielectric response of grain and should be considered to improve prediction of moisture

by permittivity measure.

56

Table 5: Fitting parameters for simple linear regression (Equations 26 and 27) of moisture against permittivity.

DensityCorrectionandDensityIndependenceMethodsDensity in Complete Models

The ASABE standard on dielectric properties of seeds cites Nelson's work on a

calibration equation for shelled, hybrid yellow-dent field corn (ASABE, 2005). The

general form of the equation is:

(29)

with:

(30)

ASABE cites coefficients for 20MHz, which result in the relation illustrated in Figure 26.

Dielectric constant values predicted by Equation 29 were similar across all frequencies

examined with the instrument; the difference in calculated versus observed dielectric

57

constant values would require a doubling of moisture. ASABE standard D293.2 notes

that this calibration was specified for temperatures above 25°C and bulk densities below

0.74g/cm3 (ASABE, 2005). Both of these ranges were exceeded by the data set. Noting

the narrow range of this model and in particular, the non-triviality of isolating moisture

from this relationship, it was determined that this calibration is not useful for the

instrument being used in this study and in general for prediction of moisture. Additional

density prediction functions will be discussed below.

!

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3.5 4.0 4.5

4.0

4.2

4.4

4.6

4.8

ASABE D293.2 Prediction of Relative Dielectric Constant, !r' at 20MHz

Measured Relative Dielectric Constant, !rmeas'

Pre

dic

ted R

ela

tive

Die

lectr

ic C

onsta

nt, ! r

pre

d'

1:1 for !rpred' and !rmeas

'

Figure 26: ASABE predicted versus measured relative dielectric constant.

Funk cites the use of the Landau and Lifshitz, Looyenga (LLL) dielectric mixture

equation as a useful correction to bulk density. The model is particularly useful for

differences due to moisture level, differences between samples and sample presentation:

58

(31)

where and are the sample and target bulk densities, respectively (Funk et al.,

2007). Using this correction and applying the result to a linear regression of moisture and

dielectric constant, the improvement is significant. Figure 27 illustrates how at certain

frequencies, this density correction can improve SEC by more than 40%. This correction

has an insignificant effect on the dielectric loss factor and its relationship with moisture.

3.6 3.8 4.0 4.2 4.4

16

17

18

19

Moisture predicted by !r' at 10240kHz, LLL Density Correction

Relative Dielectric Constant, !r'

Mois

ture

Conte

nt (%

), %

M

Original Dielectric Constant

LLL Modified

Figure 27: Landau and Lifshitz, Looyenga density correction improves overall fit of dielectric constant to moisture.

59

Stepping back from the complexity of these higher order models, a simple linear

regression with terms for density was run to compare to the LLL method.

and (32, 33)

It is shown in Table 6 that performance of the linear term in Equations 32 and 33 is a

marginally more robust method for density correction than the LLL method of correcting

permittivity.

Another density correction method is to "shrink" the grain to a target moisture.

This is accomplished by scaling the density based on the sample’s proximity to the

standard moisture (Equation 34).

(34)

Figure 28 shows the resulting densities compared to the original measured density. This

method further reduced SEC to 0.25% for all frequencies of the dielectric constant.

Table 6: Comparison of calibration error for several density terms to moisture and permittivity regressions.

60

!

!

!

!

!

!

!

!!

!

!

!

0.71 0.72 0.73 0.74 0.75 0.76 0.77

0.7

00.7

10.7

20.7

30.7

40.7

50.7

6

Shrinkage: Density Correction For Moisture Variation

Bulk Density Measured (g cm3) , !

Bulk

Density C

orr

ecte

d to 1

5.5

% G

rain

(g

cm

3),

!

sh

run

k

! 15%

16%

17%

18%

19%

Figure 28: Bulk density of grain shrunk for linear regression moisture predictor.

Instrument's Built-In Density Independent Function The instrument had previously used an algorithm for predicting moisture based on

third order polynomial fit of the ratio between the dielectric constant at two frequencies

and a linear temperature compensation factor. This model was developed as a

preliminary density independent function, allowing moisture to be determined in spite of

fluctuating sample bulk densities.

61

(35)

where

€

Φ =10 ⋅ 1−′ ε 400kHz′ ε 12.5kHz

(36)

This model was non-specific for its frequency selection, so regressions as in

Equation 36, were calculated for all permittivity ratios, both dielectric constant and loss

factor. This model’s SEC values were consistent with models requiring a known density

(Table 6). However, there was still some density dependence in the model when using

ratios of the dielectric loss factor for . Regression with an additional linear term for

density improved prediction intervals by 12% for the best ratios of dielectric loss factors.

The dielectric constant ratios were improved less (3%) and such improvement could be

explained by the addition of a term to the regression model. Figure 29 shows the

contours of the SEC for the complete data set of predictors by frequency for the FT

sample cell. This gives a general overview of what frequency ratios are most effective

for the density independent function, . The FP sensor cell had similar performance to

the FT sensor cell in regions where produced a useful result.

62

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

5 10 15 20

5

10

15

20

SEC Levels for Regression of

Moisture to 3rd Order Polynomial of Permittivity

Ratio Between Selected Frequencies For FT Sensor

Permittivity by Frequency and Real/Imaginary Part

Ind

ex 1

:12

= D

iele

ctr

ic C

on

sta

nt,

In

de

x 1

3:2

4 =

Lo

ss F

acto

r

Sta

nd

ard

Err

or

of

Ca

libra

tio

n f

or

Pre

dic

ted

%M

Figure 29: Contours of SEC for moisture prediction based on function; by frequency and dielectric constant or loss factor. Density Independent Models from Literature

Berbert and Stenning cite the Meyer and Schilz function as a potential density

independent function (Berbert and Stenning, 1996). They note, however that the result

has conflicting success in the literature at frequencies below 10GHz. The Meyer and

Schilz function is another simple ratio between dielectric constant and loss factor. The

63

literature also illustrates that though this function is linear in small moisture ranges, over

wide ranges it cannot be approximated with a linear regression.

(37)

!

!

!

!

!

!!

!

!

!!

!

!

!!

!

!

!

!!

!

! !

!

!

!!

!

!

!!!

!

!!

!

!

!

!

!

!

!!!

!

!

! !

!!

!!

!

!!!

! !!

!

!!!!

!

!

!! !

!

!

!

!!

!!

!!

!

!

!

!!

!

6 8 10 12 14 16

16

17

18

19

Meyer & Schilz Function at 640 kHz

Meyer & Schilz Function (dimensionless), (!'"1) !"

Me

asu

red

Mo

istu

re C

on

ten

t (%

), %

M

Figure 30: Meyer & Schilz function for predicting moisture independent of density.

Figure 30 illustrates this function for the FT sensor cell. The SEC of a linear model

based on Figure 30 is 0.43% moisture, wet basis.

The most useful work on density independence has been done by Trabelsi,

Kraszewski, and Nelson (Trabelsi et al., 1999b). Extending the ideas from the Meyer &

Schilz equation, they designed a clever method for microwave frequencies where

permittivities are plotted in the complex plane. The bulk densities for measured products

64

are divided through the dielectric constant and the dielectric loss factor. The result is a

plot with a frequency dependent slope that is density dependent, shown in Figure 31.

!!!!

!!

!

!

!!

!!

!!!!

!!!

!

!!

!!

!!

!!

!!! !

!!!!

!

!!!

!!! !

!!!!

!!!!

!

!!

!

! !!!

!!

!!

!

!!

!

!!! !

!

!

!

!!

!

!

!

!!

!!

6.0 6.5 7.0 7.5

0.4

0.6

0.8

1.0

1.2

Complex Permittivity Normalized to Bulk Density at 320kHz, !'/" vs !"/"

!'/", " in g cm3

!"/"

¯ Slope: 0.509

Figure 31: Complex plane plot of permittivity divided by density.

This slope gives rise to a function:

(38)

which has been shown to be a linear predictor of moisture (Trabelsi et al., 1999b). In

Trabelsi's work in the microwave range, the slope of over frequency was monotonic

and could be fit to a simple linear regression, allowing the complete quantization of

moisture at multiple frequencies. However, as is shown in Figure 32 the RF

65

permittivities were not consistent with this result. Instead the values of increased to

160kHz and then decreased with increasing frequency.

!!!

!!

!!!

!!

!

!

!

!

!

!

!

!

!!

!

!

!

!

!

!

!

!

!

!

!

!

!

!!

10 20 40 80 160 320 640 2560 10240

0.2

0.3

0.4

0.5

Frequency Coefficient, af for ! Function in FT Sensor Cell

Frequency (kHz), f

Fre

qu

en

cy C

oe

ffic

ien

t (d

ime

nsio

nle

ss),

af

Figure 32: values for function (Equation 38).

Figure 33 shows the function plotted against moisture. Table 7 shows the SEC for

each frequency.

66

!

!

!

!

!

!!

!

!

!!

!

!

!!

!

!

!

!!

!

!!

!

!

!!

!

!

! !!

!

!!

!

!

!

!

!

!

!!!

!

!

!!

!!

!!

!

!! !

!! !

!

! !!!

!

!

!!!

!

!

!

!!

!!!!

!

!

!

!!

!

0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30

16

17

18

19

Moisture Predicted (%M) by ! Function at 320kHz

! (unitless), Density Independent Function

Mo

istu

re (

%),

%M

R2: 0.83

SEC: 0.38

Figure 33: Results of function moisture prediction.

Table 7: SEC results of function moisture prediction for FT and FP sensor cells.

TemperatureDependenceThe data set had a limited temperature variation by design. The range of

temperatures obtained in this data spans 7.25 to 11ºC, Figure 34. This study was not

67

designed to test temperature dependence. Adding temperature terms to linear regressions

for this data set generally yielded statistically insignificant factors. One notable

exception was the temperature dependence when the term was added to the above

function. Table 8 shows values for the temperature term in the regression based on the

model:

(39)

Past research indicates that these values are appropriate (Funk, 2001; Funk et al., 2007;

Trabelsi and Nelson, 2004). The cited findings have previously found a linear correction

factor of approximately -0.10% moisture per degree Centigrade.

Table 8: Temperature coefficients and their significance.

68

0 20 40 60 80

89

10

11

Temperature Variations in Dielectric Corn Measurements

Sample

Te

mp

era

ture

(D

eg

C)

Figure 34: Temperature variations across all grain samples.

DensityDependenceBulk density prediction by permittivity based instrumentation has been well

studied (Nelson, 2006; Nelson, 2005; Trabelsi et al., 2001a; Trabelsi et al., 1999b).

Density models for correlation to permittivity attempt to remove the effect that

temperature and moisture have on the measured dielectric constant and loss factors either

explicitly (by linear or non-linear models including these effects directly) or implicitly

(using derived relationships).

69

Explicit Models The most basic model for removing moisture and temperature dependence from

the measured dielectric constant and loss factor is a simple linear regression. Equations

40 and 41 show this model.

and (40, 41)

With the small temperature variations in the data, the temperature term ( ) was not

significant. A revised regression without the temperature term yielded an SEC of 0.0089

g/cm3 (about 1.2% of the measured density).

The instrument’s creator used a variation on the simple linear model. The model

used is shown in:

(42)

The model performance is comparable to that of the simple linear model. SEP is shown

in Table 9 (1.6% of total value). This model’s performance significantly degraded with

decreasing instrument frequency.

Nelson and Funk make the case for fitting the density as a linear function of the

cube root of dielectric constant based on the results of the Landau and Lifshitz, Looyenga

dielectric mixture equation (Funk et al., 2007; Nelson, 2005). Allowing for explicit

temperature and moisture correction, the previous model becomes:

(43)

This model had an almost identical response with an SEC of 0.0088 g/cm3.

What is much more interesting is the result of a variation on Equation 42 (the

previously used instrument model) when the logarithm is replaced with the cube root:

70

(44)

This model reduced the SEC to 0.0045 g/cm3, which was a very significant reduction in

error.

Psi Function and Density Trabelsi’s work on determining a density independent function included deriving

a prediction of density from the same relationship (Trabelsi et al., 1999b).

solved for becomes: (45, 46)

This model had very significant limitations at the limits of the frequency range tested, but

SEC for the 160 to 640kHz range was ~0.015 g/cm3.

Table 9: SEC of various density regression models.

Conclusions

Permittivity measurements were taken at 10kHz to 20MHz in octave steps on

flowing grain samples ranging from 15 to 19% wet basis moisture and 0.70 to 0.77 g/cm3.

Multiple calibrations were compared and performance evaluated for predicting moisture

and density simultaneously using the measured permittivity. The apparatus in this study

allowed for flowing samplings of grain leading to more robust calibrations. Though

71

modest in range of moistures and densities, the results of models allowing simultaneous

determination of moisture content and bulk density were comparable to results in

published literature.

Moisture predictions were obtained using almost any prediction model analyzed

in this study as long as the frequency was selected carefully. For density, however, the

cubic root model in Equation 44 is a significant improvement over existing models,

halving the SEC. This study raised interesting questions about the relationship between

different sensing electrode configurations in the FT and FP sensing cells. Geometry,

frequency, and dielectric strength combined to influence how sensing configurations

affect the observed relative permittivity. Finally, the results of these experiments have

verified that many models in published literature based on microwave frequencies

(300MHz to 300GHz) perform well at radio frequencies (3kHz to 300MHz).

Future work may do well to investigate some of the initial studies in this research,

which examined fertilizer and soils. Necessary research would control for moisture,

temperature, and density while measuring complex permittivity. Classifying by grain

type and grain variety would require a large pool of controlled data (again, moisture,

temperature, and density) given the findings of this research. Additional research is

required to expand the newfound cubic root model (Equation 44) for density prediction to

other materials beyond corn and to verify the effect of temperature on this model. Other

research has suggested that VHF (30-300MHz) is more adept at higher moisture grains

than LF/MF/HF (30kHz-30MHz). This could be verified by examining the response of

the instrumentation from this study at higher moisture contents (20-30%, wet basis).

Finally, additional moistures of grains should be examined to verify that extrapolating

72

models within this research to wider ranges could be done and to verify what effect this

has on the error rates of said models.

73

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